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Exponential Growth and Decay Formula:
Initial Starting Value # of times it grows or decays Growth/Decay Factor
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Exponential Growth Growth Factor: b = 1 + Rate of Growth $10 is invested in a savings account where is grows 5% per year. What is the y –intercept?
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Exponential Decay Decay Factor: b = 1 - Rate of Growth 10 grams of a particular liquid decays at a rate of 75% per day.
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Practice: Monthly benefits for Social Security in May were $23,307 million. Since then, benefits have increased about 5.4% per year. a) Write an exponential function to model the growth of monthly Social Security benefits paid each year. (use millions in your answer!) y = 23,307( )x y = 23,307(1.054)x b) If benefits continue to grow at this rate, when will the monthly Social Security benefits reach $50,000 million? 50,000 = 23,307(1.054)x Graph y = 23,307(1.054)x and y = 50,000 2) Solve = 1.054x through guess and check
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There is 81% of the fund LEFT each year
In 1984, funds for the Emergency Food Assistance program were about $1,075 million. Since 1984, this fund has decreased about 19% per year. a) Write an exponential function to model this situation. Y= 1,075( )x y = 1,075(0.81)x There is 81% of the fund LEFT each year b) Estimate the funds available for the Emergency Food Assistance program this year. Y = 1075(0.81)24 million Or graph the equation and TRACE with x = 24
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